Definition:Constructible Point in Plane

Definition

Let $\CC$ be a Cartesian coordinate plane.

Let $S$ be a set of points in $\CC$.

Let $P$ be a point in $\CC$.

Let there exist a compass and straightedge construction for $P$ from a line segment $AB$, where $A, B \in S$

Then $P$ is defined as constructible from $S$.

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 40$. Construction with Ruler and Compasses